If people want a closely integrated whole,
then it's true you can't have any and all parts just included. But the British Empire in OTL was never "a united nation"; hardly any empire ever is. An empire is most often a multinational affair. The British Empire certainly was. In any case, an Imperial Federation
in no way implies "something in integration terms between the EU and the USA". That wasn't the plan historically, and it isn't even realistic in terms of a "white dominions only" kind of arrangement.
And just to make something a bit clear: the difference between a federation and a confederation has to do with sovereignty, not with degree of integration. A confederation is an amalgation of sovereign states that voluntarily grant power to a shared government (but by definition retain sovereignty, and can thus demand that authority back, and freely withdraw from the confederation). The EU is actually a confederation. A federation is a system whereby the constituent states and a central goverment share sovereignty, and each has an allocated 'sphere'; states cannot simply demand full sovereignty back, and withdrawing from the federation isn't automatically possible.
The point is that a federation can be incredibly loosely organised, and a confederation can end up being more tight. Legally, the British Empire in a situation such as the one discussed here, would almost certainly be a federation. I'm just betting that certain countries would get some kind of 'associate member' status. That just makes the most sense. Bottom line is that "it's not united/integrated enough!" is not a valid objection-- because the kind of unity some people here seem to desire
was never the plan in OTL.
Anyway, if
@Joshuapooleanox wants a federation with certain geographical limitations, that's perfectly valid. All I pointed out was that it's not automatically needed to set up those limitations, and that even with those limitations in place... you're not getting anything with a level of integration akin to something in "between the EU and the USA".